A short answer is the natural way to answer a polar question (also known as a "yes/no question"), that is, a question which invites a simple yes/no answer.
Polar questions begin with an auxiliary verb or modal verb and are usually, but not always, answered with the same auxiliary/modal verb. We use ellipsis to avoid having to repeat the rest of the words in the question.
- Do you smoke? - Yes, I do/No, I don't
- Does she speak English? - Yes, she does/No, she doesn't
- Are you ready? - Yes, I am/No, I'm not/Yes, we are/No, we aren't
It is important that students learn to include the modal verb after "yes" or "no" as answering with a simple "yes" or "no" will be taken by a native speaker to indicate that the speaker is either being rude or has no interest in the conversation and the conversation will end abruptly, with both parties possibly feeling mildly offended. Obviously the speaker can omit the "I do" part if (s)he then goes on to say something else immediately afterwards:
- Does she speak English? - No, but she's started taking lessons.
Students should also take care to repeat the modal or auxiliary and not the verb. In other words, the answer to the question Do you like chocolate? is Yes, I do. (*).
Not all questions beginning with Did/Are you...? etc. lead to a simple yes/no answer. One way of getting students to respond more fully is by asking "either/or" questions, for instance, Did you..., or were you..?
Depending on context, some polar questions, such as Would you like a cup of tea?, require a totally different response, i.e. Yes, please./No, thanks.